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<div class="title">floyd_warshall.h</div>  </div>
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<a href="floyd__warshall_8h.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno">    1</span>&#160;<span class="comment">/*</span></div>
<div class="line"><a name="l00002"></a><span class="lineno">    2</span>&#160;<span class="comment"> * Copyright 2016- huaxz &lt;huaxz1986@163.com&gt;</span></div>
<div class="line"><a name="l00003"></a><span class="lineno">    3</span>&#160;<span class="comment"> *</span></div>
<div class="line"><a name="l00004"></a><span class="lineno">    4</span>&#160;<span class="comment"> * This program is free software: you can redistribute it and/or modify</span></div>
<div class="line"><a name="l00005"></a><span class="lineno">    5</span>&#160;<span class="comment"> * it under the terms of the GNU General Public License as published by</span></div>
<div class="line"><a name="l00006"></a><span class="lineno">    6</span>&#160;<span class="comment"> * the Free Software Foundation, either version 2 of the License, or</span></div>
<div class="line"><a name="l00007"></a><span class="lineno">    7</span>&#160;<span class="comment"> * (at your option) any later version.</span></div>
<div class="line"><a name="l00008"></a><span class="lineno">    8</span>&#160;<span class="comment"> *</span></div>
<div class="line"><a name="l00009"></a><span class="lineno">    9</span>&#160;<span class="comment"> * This program is distributed in the hope that it will be useful,</span></div>
<div class="line"><a name="l00010"></a><span class="lineno">   10</span>&#160;<span class="comment"> * but WITHOUT ANY WARRANTY; without even the implied warranty of</span></div>
<div class="line"><a name="l00011"></a><span class="lineno">   11</span>&#160;<span class="comment"> * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the</span></div>
<div class="line"><a name="l00012"></a><span class="lineno">   12</span>&#160;<span class="comment"> * GNU General Public License for more details.</span></div>
<div class="line"><a name="l00013"></a><span class="lineno">   13</span>&#160;<span class="comment"> *</span></div>
<div class="line"><a name="l00014"></a><span class="lineno">   14</span>&#160;<span class="comment"> * You should have received a copy of the GNU General Public License</span></div>
<div class="line"><a name="l00015"></a><span class="lineno">   15</span>&#160;<span class="comment"> * along with this program.  If not, see &lt;http://www.gnu.org/licenses/&gt;.</span></div>
<div class="line"><a name="l00016"></a><span class="lineno">   16</span>&#160;<span class="comment"> *</span></div>
<div class="line"><a name="l00017"></a><span class="lineno">   17</span>&#160;<span class="comment"> * Author: huaxz1986@163.com (huaxz)</span></div>
<div class="line"><a name="l00018"></a><span class="lineno">   18</span>&#160;<span class="comment"> */</span></div>
<div class="line"><a name="l00019"></a><span class="lineno">   19</span>&#160;<span class="preprocessor">#ifndef FLOYD_WARSHALL</span></div>
<div class="line"><a name="l00020"></a><span class="lineno">   20</span>&#160;<span class="preprocessor">#define FLOYD_WARSHALL</span></div>
<div class="line"><a name="l00021"></a><span class="lineno">   21</span>&#160;<span class="preprocessor">#include&lt;memory&gt;</span></div>
<div class="line"><a name="l00022"></a><span class="lineno">   22</span>&#160;<span class="preprocessor">#include&quot;<a class="code" href="header_8h.html">src/header.h</a>&quot;</span></div>
<div class="line"><a name="l00023"></a><span class="lineno">   23</span>&#160;<span class="keyword">namespace </span><a class="code" href="namespace_introduction_to_algorithm.html">IntroductionToAlgorithm</a></div>
<div class="line"><a name="l00024"></a><span class="lineno">   24</span>&#160;{</div>
<div class="line"><a name="l00025"></a><span class="lineno"><a class="line" href="namespace_introduction_to_algorithm_1_1_graph_algorithm.html">   25</a></span>&#160;    <span class="keyword">namespace </span>GraphAlgorithm</div>
<div class="line"><a name="l00026"></a><span class="lineno">   26</span>&#160;    {</div>
<div class="line"><a name="l00027"></a><span class="lineno">   27</span>&#160;</div>
<div class="line"><a name="l00029"></a><span class="lineno">   29</span>&#160;</div>
<div class="line"><a name="l00104"></a><span class="lineno">  104</span>&#160;        <span class="keyword">template</span>&lt;<span class="keyword">typename</span> GraphType&gt;</div>
<div class="line"><a name="l00105"></a><span class="lineno">  105</span>&#160;        std::pair&lt;</div>
<div class="line"><a name="l00106"></a><span class="lineno">  106</span>&#160;        std::array&lt;std::array&lt;typename GraphType::EWeightType ,GraphType::NUM&gt;,GraphType::NUM&gt;,</div>
<div class="line"><a name="l00107"></a><span class="lineno">  107</span>&#160;        std::array&lt;std::array&lt;typename GraphType::EWeightType ,GraphType::NUM&gt;,GraphType::NUM&gt;</div>
<div class="line"><a name="l00108"></a><span class="lineno">  108</span>&#160;        &gt;</div>
<div class="line"><a name="l00109"></a><span class="lineno"><a class="line" href="namespace_introduction_to_algorithm_1_1_graph_algorithm.html#ab951caca0797ff2907a180fe81609c70">  109</a></span>&#160;        <a class="code" href="namespace_introduction_to_algorithm_1_1_graph_algorithm.html#ab951caca0797ff2907a180fe81609c70">floyd_warshall</a>(std::shared_ptr&lt;GraphType&gt; graph)</div>
<div class="line"><a name="l00110"></a><span class="lineno">  110</span>&#160;        {</div>
<div class="line"><a name="l00111"></a><span class="lineno">  111</span>&#160;            <span class="keyword">typedef</span> <span class="keyword">typename</span> GraphType::EWeightType EWeightType;</div>
<div class="line"><a name="l00112"></a><span class="lineno">  112</span>&#160;            <span class="keyword">typedef</span> std::array&lt;std::array&lt;EWeightType,GraphType::NUM&gt;,GraphType::NUM&gt; MatrixType;</div>
<div class="line"><a name="l00113"></a><span class="lineno">  113</span>&#160;</div>
<div class="line"><a name="l00114"></a><span class="lineno">  114</span>&#160;            <span class="keywordflow">if</span>(!graph)</div>
<div class="line"><a name="l00115"></a><span class="lineno">  115</span>&#160;                <span class="keywordflow">throw</span> std::invalid_argument(<span class="stringliteral">&quot;floyd_warshall error: graph must not be nullptr!&quot;</span>);</div>
<div class="line"><a name="l00116"></a><span class="lineno">  116</span>&#160;            <span class="comment">//**************  初始化 D 和 P ************</span></div>
<div class="line"><a name="l00117"></a><span class="lineno">  117</span>&#160;            <span class="comment">//****  这里不能直接从图的矩阵描述中提取，因为这里要求 w(i,i)=0，而图的矩阵描述中，结点可能有指向自己的边</span></div>
<div class="line"><a name="l00118"></a><span class="lineno">  118</span>&#160;            MatrixType D,P;</div>
<div class="line"><a name="l00119"></a><span class="lineno">  119</span>&#160;            <span class="keywordflow">for</span>(<span class="keywordtype">int</span> i=0;i&lt;GraphType::NUM;i++)</div>
<div class="line"><a name="l00120"></a><span class="lineno">  120</span>&#160;                <span class="keywordflow">for</span>(<span class="keywordtype">int</span> j=0;j&lt;GraphType::NUM;j++)</div>
<div class="line"><a name="l00121"></a><span class="lineno">  121</span>&#160;                {</div>
<div class="line"><a name="l00122"></a><span class="lineno">  122</span>&#160;                    <span class="keywordflow">if</span>(i==j)</div>
<div class="line"><a name="l00123"></a><span class="lineno">  123</span>&#160;                    {</div>
<div class="line"><a name="l00124"></a><span class="lineno">  124</span>&#160;                        D[i][j]=0;</div>
<div class="line"><a name="l00125"></a><span class="lineno">  125</span>&#160;                        P[i][j]=-1;</div>
<div class="line"><a name="l00126"></a><span class="lineno">  126</span>&#160;                    }</div>
<div class="line"><a name="l00127"></a><span class="lineno">  127</span>&#160;                    <span class="keywordflow">else</span></div>
<div class="line"><a name="l00128"></a><span class="lineno">  128</span>&#160;                    {</div>
<div class="line"><a name="l00129"></a><span class="lineno">  129</span>&#160;                        <span class="keywordflow">if</span>(!graph-&gt;has_edge(i,j))</div>
<div class="line"><a name="l00130"></a><span class="lineno">  130</span>&#160;                        {</div>
<div class="line"><a name="l00131"></a><span class="lineno">  131</span>&#160;                            D[i][j]=unlimit&lt;EWeightType&gt;();</div>
<div class="line"><a name="l00132"></a><span class="lineno">  132</span>&#160;                            P[i][j]=-1;</div>
<div class="line"><a name="l00133"></a><span class="lineno">  133</span>&#160;                        }</div>
<div class="line"><a name="l00134"></a><span class="lineno">  134</span>&#160;                        <span class="keywordflow">else</span></div>
<div class="line"><a name="l00135"></a><span class="lineno">  135</span>&#160;                        {</div>
<div class="line"><a name="l00136"></a><span class="lineno">  136</span>&#160;                            D[i][j]=graph-&gt;weight(i,j);</div>
<div class="line"><a name="l00137"></a><span class="lineno">  137</span>&#160;                            P[i][j]=i;</div>
<div class="line"><a name="l00138"></a><span class="lineno">  138</span>&#160;                        }</div>
<div class="line"><a name="l00139"></a><span class="lineno">  139</span>&#160;                    }</div>
<div class="line"><a name="l00140"></a><span class="lineno">  140</span>&#160;                 }</div>
<div class="line"><a name="l00141"></a><span class="lineno">  141</span>&#160;            <span class="comment">//**************  计算矩阵D和前驱矩阵P ******************</span></div>
<div class="line"><a name="l00142"></a><span class="lineno">  142</span>&#160;            <span class="keywordflow">for</span>(<span class="keywordtype">int</span> k=0;k&lt;GraphType::NUM;k++)</div>
<div class="line"><a name="l00143"></a><span class="lineno">  143</span>&#160;            {</div>
<div class="line"><a name="l00144"></a><span class="lineno">  144</span>&#160;                MatrixType newD; <span class="comment">//  D&lt;k&gt;</span></div>
<div class="line"><a name="l00145"></a><span class="lineno">  145</span>&#160;                MatrixType newP; <span class="comment">//  P&lt;k&gt;</span></div>
<div class="line"><a name="l00146"></a><span class="lineno">  146</span>&#160;                <span class="keywordflow">for</span>(<span class="keywordtype">int</span> i=0;i&lt;GraphType::NUM;i++)</div>
<div class="line"><a name="l00147"></a><span class="lineno">  147</span>&#160;                {</div>
<div class="line"><a name="l00148"></a><span class="lineno">  148</span>&#160;                    <span class="keywordflow">for</span>(<span class="keywordtype">int</span> j=0;j&lt;GraphType::NUM;j++)</div>
<div class="line"><a name="l00149"></a><span class="lineno">  149</span>&#160;                    {</div>
<div class="line"><a name="l00150"></a><span class="lineno">  150</span>&#160;                        <span class="comment">// D中存放的是D&lt;k-1&gt;,P中存放的是P&lt;k-1&gt;</span></div>
<div class="line"><a name="l00151"></a><span class="lineno">  151</span>&#160;                        EWeightType sum=0;</div>
<div class="line"><a name="l00152"></a><span class="lineno">  152</span>&#160;                        <span class="keywordflow">if</span>(D[i][k]==unlimit&lt;EWeightType&gt;()||D[k][j]==unlimit&lt;EWeightType&gt;()||D[i][k]+D[k][j]&gt;=unlimit&lt;EWeightType&gt;())</div>
<div class="line"><a name="l00153"></a><span class="lineno">  153</span>&#160;                            sum=unlimit&lt;EWeightType&gt;();</div>
<div class="line"><a name="l00154"></a><span class="lineno">  154</span>&#160;                        <span class="keywordflow">else</span></div>
<div class="line"><a name="l00155"></a><span class="lineno">  155</span>&#160;                            sum=D[i][k]+D[k][j];</div>
<div class="line"><a name="l00156"></a><span class="lineno">  156</span>&#160;</div>
<div class="line"><a name="l00157"></a><span class="lineno">  157</span>&#160;                        <span class="keywordflow">if</span>(D[i][j]&lt;=sum) <span class="comment">// d_i_j&lt;k-1&gt; &lt;= d_i_k&lt;k-1&gt;+d_k_j&lt;k-1&gt;</span></div>
<div class="line"><a name="l00158"></a><span class="lineno">  158</span>&#160;                        {</div>
<div class="line"><a name="l00159"></a><span class="lineno">  159</span>&#160;                           newD[i][j]= D[i][j]; <span class="comment">//则 d_i_j&lt;k&gt; = d_i_j&lt;k-1&gt;</span></div>
<div class="line"><a name="l00160"></a><span class="lineno">  160</span>&#160;                           newP[i][j]= P[i][j]; <span class="comment">//则 p_i_j&lt;k&gt; = p_i_j&lt;k-1&gt;</span></div>
<div class="line"><a name="l00161"></a><span class="lineno">  161</span>&#160;                        }</div>
<div class="line"><a name="l00162"></a><span class="lineno">  162</span>&#160;                        <span class="keywordflow">else</span>  <span class="comment">// d_i_j&lt;k-1&gt; &gt; d_i_k&lt;k-1&gt;+d_k_j&lt;k-1&gt;</span></div>
<div class="line"><a name="l00163"></a><span class="lineno">  163</span>&#160;                        {</div>
<div class="line"><a name="l00164"></a><span class="lineno">  164</span>&#160;                            newD[i][j]= sum; <span class="comment">//则 d_i_j&lt;k&gt; = d_i_k&lt;k-1&gt;+d_k_j&lt;k-1&gt;</span></div>
<div class="line"><a name="l00165"></a><span class="lineno">  165</span>&#160;                            newP[i][j]= P[k][j];         <span class="comment">//则 p_i_j&lt;k&gt; = p_k_j&lt;k-1&gt;</span></div>
<div class="line"><a name="l00166"></a><span class="lineno">  166</span>&#160;                        }</div>
<div class="line"><a name="l00167"></a><span class="lineno">  167</span>&#160;                     }</div>
<div class="line"><a name="l00168"></a><span class="lineno">  168</span>&#160;                }</div>
<div class="line"><a name="l00169"></a><span class="lineno">  169</span>&#160;                D=newD;</div>
<div class="line"><a name="l00170"></a><span class="lineno">  170</span>&#160;                P=newP;</div>
<div class="line"><a name="l00171"></a><span class="lineno">  171</span>&#160;            }</div>
<div class="line"><a name="l00172"></a><span class="lineno">  172</span>&#160;            <span class="keywordflow">return</span> std::make_pair(D,P);</div>
<div class="line"><a name="l00173"></a><span class="lineno">  173</span>&#160;        }</div>
<div class="line"><a name="l00174"></a><span class="lineno">  174</span>&#160;    }</div>
<div class="line"><a name="l00175"></a><span class="lineno">  175</span>&#160;}</div>
<div class="line"><a name="l00176"></a><span class="lineno">  176</span>&#160;<span class="preprocessor">#endif // FLOYD_WARSHALL</span></div>
<div class="line"><a name="l00177"></a><span class="lineno">  177</span>&#160;</div>
<div class="ttc" id="header_8h_html"><div class="ttname"><a href="header_8h.html">header.h</a></div></div>
<div class="ttc" id="namespace_introduction_to_algorithm_html"><div class="ttname"><a href="namespace_introduction_to_algorithm.html">IntroductionToAlgorithm</a></div><div class="ttdoc">Namespace of IntrodunctionToAlgorithm. </div><div class="ttdef"><b>Definition:</b> <a href="longest__common__subsequence_8h_source.html#l00024">longest_common_subsequence.h:24</a></div></div>
<div class="ttc" id="namespace_introduction_to_algorithm_1_1_graph_algorithm_html_ab951caca0797ff2907a180fe81609c70"><div class="ttname"><a href="namespace_introduction_to_algorithm_1_1_graph_algorithm.html#ab951caca0797ff2907a180fe81609c70">IntroductionToAlgorithm::GraphAlgorithm::floyd_warshall</a></div><div class="ttdeci">std::pair&lt; std::array&lt; std::array&lt; typename GraphType::EWeightType,GraphType::NUM &gt;, GraphType::NUM &gt;, std::array&lt; std::array&lt; typename GraphType::EWeightType,GraphType::NUM &gt;, GraphType::NUM &gt; &gt; floyd_warshall(std::shared_ptr&lt; GraphType &gt; graph)</div><div class="ttdoc">floyd_warshall：返回所有节点对的最短路径的floyd_warshall算法。算法导论25章25.2节 </div><div class="ttdef"><b>Definition:</b> <a href="floyd__warshall_8h_source.html#l00109">floyd_warshall.h:109</a></div></div>
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